finMath lib documentation
net.finmath.montecarlo.interestrate

## Class LIBORMarketModelWithTenorRefinement

• All Implemented Interfaces:
TermStructureModelInterface, AbstractModelInterface

public class LIBORMarketModelWithTenorRefinement
extends AbstractModel
implements TermStructureModelInterface
Implements a discretized Heath-Jarrow-Morton model / LIBOR market model with dynamic tenor refinement, see https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2884699.

In its default case the class specifies a multi-factor LIBOR market model, that is $$L_{j} = \frac{1}{T_{j+1}-T_{j}} ( exp(Y_{j}) - 1 )$$, where $dY_{j} = \mu_{j} dt + \lambda_{1,j} dW_{1} + \ldots + \lambda_{m,j} dW_{m}$
The model uses an AbstractLIBORCovarianceModel for the specification of 1,j,...,λm,j) as a covariance model. See AbstractModelInterface for details on the implemented interface

The model uses an AbstractLIBORCovarianceModel as a covariance model. If the covariance model is of type AbstractLIBORCovarianceModelParametric a calibration to swaptions can be performed.
Note that λ may still depend on L (through a local volatility model).
The simulation is performed under spot measure, that is, the numeraire is $$N(T_{i}) = \prod_{j=0}^{i-1} (1 + L(T_{j},T_{j+1};T_{j}) (T_{j+1}-T_{j}))$$. The map properties allows to configure the model. The following keys may be used:
• liborCap: An optional Double value applied as a cap to the LIBOR rates. May be used to limit the simulated valued to prevent values attaining POSITIVE_INFINITY and numerical problems. To disable the cap, set liborCap to Double.POSITIVE_INFINITY.

The main task of this class is to calculate the risk-neutral drift and the corresponding numeraire given the covariance model. The calibration of the covariance structure is not part of this class.
Version:
1.2
Author:
Christian Fries
The interface for numerical schemes., The interface for models provinding parameters to numerical schemes., https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2884699
• ### Constructor Detail

• #### LIBORMarketModelWithTenorRefinement

public LIBORMarketModelWithTenorRefinement(TimeDiscretizationInterface[] liborPeriodDiscretizations,
Integer[] numberOfDiscretizationIntervalls,
AnalyticModelInterface analyticModel,
ForwardCurveInterface forwardRateCurve,
DiscountCurveInterface discountCurve,
TermStructureCovarianceModelInterface covarianceModel,
LIBORMarketModelWithTenorRefinement.CalibrationItem[] calibrationItems,
Map<String,?> properties)
throws CalculationException
Creates a model for given covariance. Creates a discretized Heath-Jarrow-Morton model / LIBOR market model with dynamic tenor refinement, see https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2884699.
If calibrationItems in non-empty and the covariance model is a parametric model, the covariance will be replaced by a calibrate version of the same model, i.e., the LIBOR Market Model will be calibrated.
The map properties allows to configure the model. The following keys may be used:
• liborCap: An optional Double value applied as a cap to the LIBOR rates. May be used to limit the simulated valued to prevent values attaining POSITIVE_INFINITY and numerical problems. To disable the cap, set liborCap to Double.POSITIVE_INFINITY.
• calibrationParameters: Possible values:
• Map<String,Object> a parameter map with the following key/value pairs:
• accuracy: Double specifying the required solver accuracy.
• maxIterations: Integer specifying the maximum iterations for the solver.
Parameters:
liborPeriodDiscretizations - A vector of tenor discretizations of the interest rate curve into forward rates (tenor structure), finest first.
numberOfDiscretizationIntervalls - A vector of number of periods to be taken from the liborPeriodDiscretizations.
analyticModel - The associated analytic model of this model (containing the associated market data objects like curve).
forwardRateCurve - The initial values for the forward rates.
discountCurve - The discount curve to use. This will create an LMM model with a deterministic zero-spread discounting adjustment.
covarianceModel - The covariance model to use.
calibrationItems - The vector of calibration items (a union of a product, target value and weight) for the objective function sum weight(i) * (modelValue(i)-targetValue(i).
properties - Key value map specifying properties like measure and stateSpace.
Throws:
CalculationException - Thrown if the valuation fails, specific cause may be available via the cause() method.
• ### Method Detail

• #### getNumeraire

public RandomVariableInterface getNumeraire(double time)
throws CalculationException
Return the numeraire at a given time. The numeraire is provided for interpolated points. If requested on points which are not part of the tenor discretization, the numeraire uses a linear interpolation of the reciprocal value. See ISBN 0470047224 for details.
Specified by:
getNumeraire in interface AbstractModelInterface
Parameters:
time - Time time t for which the numeraire should be returned N(t).
Returns:
The numeraire at the specified time as RandomVariableInterface
Throws:
CalculationException - Thrown if the valuation fails, specific cause may be available via the cause() method.
• #### getInitialState

public RandomVariableInterface[] getInitialState()
Description copied from interface: AbstractModelInterface
Returns the initial value of the state variable of the process Y, not to be confused with the initial value of the model X (which is the state space transform applied to this state value.
Specified by:
getInitialState in interface AbstractModelInterface
Returns:
The initial value of the state variable of the process Y(t=0).
• #### getDrift

public RandomVariableInterface[] getDrift(int timeIndex,
RandomVariableInterface[] realizationAtTimeIndex,
RandomVariableInterface[] realizationPredictor)
Return the complete vector of the drift for the time index timeIndex, given that current state is realizationAtTimeIndex. The drift will be zero for rates being already fixed. The method currently provides the drift for either Measure.SPOT or Measure.TERMINAL - depending how the model object was constructed. For Measure.TERMINAL the j-th entry of the return value is the random variable $\mu_{j}^{\mathbb{Q}^{P(T_{n})}}(t) \ = \ - \mathop{\sum_{l\geq j+1}}_{l\leq n-1} \frac{\delta_{l}}{1+\delta_{l} L_{l}(t)} (\lambda_{j}(t) \cdot \lambda_{l}(t))$ and for Measure.SPOT the j-th entry of the return value is the random variable $\mu_{j}^{\mathbb{Q}^{N}}(t) \ = \ \sum_{m(t) < l\leq j} \frac{\delta_{l}}{1+\delta_{l} L_{l}(t)} (\lambda_{j}(t) \cdot \lambda_{l}(t))$ where $$\lambda_{j}$$ is the vector for factor loadings for the j-th component of the stochastic process (that is, the diffusion part is $$\sum_{k=1}^m \lambda_{j,k} \mathrm{d}W_{k}$$). Note: The scalar product of the factor loadings determines the instantaneous covariance. If the model is written in log-coordinates (using exp as a state space transform), we find $$\lambda_{j} \cdot \lambda_{l} = \sum_{k=1}^m \lambda_{j,k} \lambda_{l,k} = \sigma_{j} \sigma_{l} \rho_{j,l}$$. If the model is written without a state space transformation (in its orignial coordinates) then $$\lambda_{j} \cdot \lambda_{l} = \sum_{k=1}^m \lambda_{j,k} \lambda_{l,k} = L_{j} L_{l} \sigma_{j} \sigma_{l} \rho_{j,l}$$.
Specified by:
getDrift in interface AbstractModelInterface
Parameters:
timeIndex - Time index i for which the drift should be returned μ(ti).
realizationAtTimeIndex - Time current forward rate vector at time index i which should be used in the calculation.
realizationPredictor - The given realization at timeIndex+1 or null if no predictor is available.
Returns:
The drift vector μ(ti) as RandomVariable[]
The calculation of the drift is consistent with the calculation of the numeraire in getNumeraire., The factor loading $$\lambda_{j,k}$$.

int componentIndex,
RandomVariableInterface[] realizationAtTimeIndex)
Description copied from interface: AbstractModelInterface
This method has to be implemented to return the factor loadings, i.e. the coefficient vector
λj = (λ1,j, ..., λm,j) such that X = f(Y) and
dYj = μj dt + λ1,j dW1 + ... + λm,j dWm
in an m-factor model. Here j denotes index of the component of the resulting process.
Specified by:
Parameters:
timeIndex - The time index (related to the model times discretization).
componentIndex - The index j of the driven component.
realizationAtTimeIndex - The realization of X at the time corresponding to timeIndex (in order to implement local and stochastic volatlity models).
Returns:
• #### applyStateSpaceTransform

public RandomVariableInterface applyStateSpaceTransform(int componentIndex,
RandomVariableInterface randomVariable)
Description copied from interface: AbstractModelInterface
Applies the state space transform fi to the given state random variable such that Yi → fi(Yi) =: Xi.
Specified by:
applyStateSpaceTransform in interface AbstractModelInterface
Parameters:
componentIndex - The component index i.
randomVariable - The state random variable Yi.
Returns:
New random variable holding the result of the state space transformation.
• #### getStateVariable

public RandomVariableInterface getStateVariable(int timeIndex,
double periodStart,
double periodEnd)
• #### getLIBOR

public RandomVariableInterface getLIBOR(int timeIndex,
double periodStart,
double periodEnd)
• #### getNumberOfLibors

public int getNumberOfLibors()
• #### clone

public Object clone()
Overrides:
clone in class Object
• #### getCovarianceModel

public TermStructureCovarianceModelInterface getCovarianceModel()
Returns the term structure covariance model.
Returns:
the term structure covariance model.